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0ltthetaltpi/2, if x=sum(n=0)^inftycos^(...

`0ltthetaltpi/2, if x=sum_(n=0)^inftycos^(2n)theta,y=sum_(n=0)^inftysin^(2n)theta,z=sum_(n=0)^inftycos^(2n)thetasin^(2n)theta`

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If x= sum_(n=0)^(oo) cos ^(2n)theta , y = sum _(n=o) ^(oo) sin ^(2n)theta, z= sum _(n=0)^(oo) cos ^(2n)theta.sin ^(2n)theta and 0 lt theta lt (pi)/(2) then-

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The value of [sum_(n=1)^(10)int_(-2n-1)^(-2n)sin^(27)x dx+sum_(n=1)^(10)int_(2n)^(2n+1)sin^(27)xdx] is equal to -

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If log(2)(5.2^(x)+1),log(4)(2^(1-x)+1) and 1 are in A.P,then x equals

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  2. Find the geometric series whose 5th and 8th terms are 80 and 640 respe...

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  3. 0ltthetaltpi/2, if x=sum(n=0)^inftycos^(2n)theta,y=sum(n=0)^inftysin^(...

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  4. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

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  5. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

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  6. The 5th, 8th and 11th terms of a GP are a,b,c respectively. Show that...

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  7. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

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  8. If p be the first of n arithmetic means between two numbers and q be t...

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  9. Find the centre and radius of the circle: (x+5)^2+(y-3)^2=20

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  10. The interior angles of a polygon are in arithmetic progression. The sm...

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  11. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

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  12. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

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  13. Find three numbers a,b,c between 2 & 18 such that; their sum is 25; th...

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  14. The sum of 50 terms of the series 1+2(1+1/(50))+3(1+1/(50))^2+ is giv...

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  15. The sum of 50 terms of the series 3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+...

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  16. Which term of the AP 3,10, 17,... will be 84 more than its 13th term?

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  17. The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...

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  18. If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmet...

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  19. Find the number of multiples of 4 lies between 10 and 250.

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  20. Find the sum 3/(1xx2)xx1/2+4/(2xx3)xx(1/2)^2+5/(3xx4)xx(1/2)^3+ to n t...

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